An elementary proof of the convergence of iterated exponentials.
An elementary proof of the Harnack inequality for non-negative infinity-superharmonic functions.
An elementary proof of the one-dimensional Rademacher theorem
An elementary short proof of the one-dimensional Rademacher theorem on differentiability of Lipschitz functions is given.
An elementary proof of the preservation of Lipschitz constants by the Meyer-König and Zeller operators.
An elementary proof of the theorem that absolute gauge integrability implies Lebesgue integrability
It is commonly known that absolute gauge integrability, or Henstock-Kurzweil (H-K) integrability implies Lebesgue integrability. In this article, we are going to present another proof of that fact which utilizes the basic definitions and properties of the Lebesgue and H-K integrals.
An Elementary Treatise on the Integral Calculus [Book]
An equation in the left and right fractional derivatives of the same order
An Equation With Left and Right Fractional Derivatives
An even easier proof of monotonicity of Stolarsky means
An example concerning small changes of commuting functions
An example of a continuous function without the usual, the approximative and the distributional derivative
An example of a function which is locally constant in an open dense set, everywhere differentiable but not constant
An example of a genuinely discontinuous generically chaotic transformation of the interval
It is proved that a piecewise monotone transformation of the unit interval (with a countable number of pieces) is generically chaotic. The Gauss map arising in connection with the continued fraction expansions of the reals is an example of such a transformation.
An example of infinitely many sinks for smooth interval maps.
An Expansion Formula for Fractional Derivatives and its Application
An expansion formula for fractional derivatives given as in form of a series involving function and moments of its k-th derivative is derived. The convergence of the series is proved and an estimate of the reminder is given. The form of the fractional derivative given here is especially suitable in deriving restrictions, in a form of internal variable theory, following from the second law of thermodynamics, when applied to linear viscoelasticity of fractional derivative type.
An extension and a refinement of van der Corput's inequality.
An extension of a theorem of Marcinkiewicz and Zygmund on differentiability
Let f be a measurable function such that at each point x of a set E, where k is a positive integer, λ > 0 and is the symmetric difference of f at x of order k. Marcinkiewicz and Zygmund [5] proved that if λ = k and if E is measurable then the Peano derivative exists a.e. on E. Here we prove that if λ > k-1 then the Peano derivative exists a.e. on E and that the result is false if λ = k-1; it is further proved that if λ is any positive integer and if the approximate Peano derivative...
An extension of Brunovský's Scorza-Dragoni type theorem for unbounded set-valued functions
An extension of Chebyshev's inequality and its connection with Jensen's inequality.
An extension of results of A. McD. Mercer and I. Gavrea.